beat_diff_prime
37 is prime. Researchers on the Gap-45 safety interlock cite it to keep beat differences irreducible under the σ-constraint. The proof is a direct term-mode computation via native_decide that evaluates the primality predicate.
claimThe natural number 37 is prime.
background
The SafetyInterlock module proves that the Gap-45 uncomputability barrier together with σ-conservation forms a safety interlock for high-coherence operation. Its key proved results include gcd(8,45)=1, lcm(8,45)=360, and the primality of the beat difference 37. The sole upstream dependency is the transparent alias Prime for Nat.Prime.
proof idea
The proof is a one-line term that applies native_decide to decide the primality predicate on 37.
why it matters in Recognition Science
This result is listed among the proved key results in the Safety Interlock module. It supports the structural impossibility of weaponization by keeping the 37-beat difference prime and irreducible. It directly fills the Gap-45 component of the interlock.
scope and limits
- Does not prove primality for any integer other than 37.
- Does not derive the integer 37 from Gap-45 parameters inside this declaration.
- Does not address physical constants or coherence levels.
formal statement (Lean)
33theorem beat_diff_prime : Nat.Prime 37 := by native_decide
proof body
Term-mode proof.
34
35/-! ## σ-Destabilization (Proved) -/
36